reserve X for set;

theorem
  for X be non empty set holds InclPoset X is with_infima implies for x,
  y be Element of InclPoset X holds x "/\" y c= x /\ y
proof
  let X be non empty set;
  assume
A1: InclPoset X is with_infima;
  let x,y be Element of InclPoset X;
  x "/\" y <= y by A1,YELLOW_0:23;
  then
A2: x "/\" y c= y by Th3;
  x "/\" y <= x by A1,YELLOW_0:23;
  then x "/\" y c= x by Th3;
  hence thesis by A2,XBOOLE_1:19;
end;
